570 



SCIENTIFIC THOUGHT. 



course of the last hundred years much has been done to 

 make it more easily understood. 



James Bernoulli had already in his celebrated book 

 which bears the title, 'De arte conjectandi,' promised 

 to show the application of the mathematical doctrine 

 of probability to political, moral, and economical sub- 

 jects, 1 but the fourth and last part of the book which 

 was to give this, remained unfinished. It was left to 

 his successors, notably to Daniel Bernoulli, to take up 

 this side of the question. But the first practical states- 

 condorcet. man who as we are told by Condorcet 2 held the 



1838), still rank with the best 

 that has been written. Stanley 

 Jevons sums up his opinion in the 

 words : " This theory appears to me 

 the noblest creation of the human 

 intellect, and it passes my concep- 

 tion how two men possessing such 

 high intelligence as Auguste Comte 

 and J. S. Mill could have been 

 found depreciating it, or even 

 vainly attempting to question its 

 validity. To eulogise the theory 

 is as needless as to eulogise reason 

 itself " (' Principles of Science,' vol. 

 i. p. 227). 



1 James Bernoulli (1654-1705) 

 was the eldest of the celebrated 

 family of mathematicians. Daniel, 

 his nephew, lived half a century 

 later (1700-82). The 'Are Con- 

 jectandi ' was published posthum- 

 ously in 1713 by Nicholas, another 

 nephew of the author. In a letter 

 to Leibniz the author says : " Ab- 

 solvi jam maximam libri partem, 

 sed deest adhuc prsecipua, qua 

 artis conjectandi principia etiam 

 ad civilia, moral ia, et oeconomica 

 applicare doceo." Daniel Bernoulli, 

 as we saw above (vol. i., chap. v. p. 

 434), was the father of the kinetic 

 theory of gases, of which more 

 hereafter. He was also the first 

 to make a distinction between 



mathematical and moral expecta- 

 tion, a difference which led 

 Laplace to distinguish between 

 " fortune physique " and " fortune 

 morale," to which reference was 

 made in connection with Fechner's 

 psycho-physical measurements. 



2 ' Essai sur 1'application de 

 PAnalyse a la Probability des De- 

 cisions, Rendues a la pluralite 

 des voix' (Paris, 1785): " Un 

 grand homme, dont je regretterai 

 toujours les legons, les exemples, 

 et surtout 1'amitie, e"tait persuade 

 que les verites des sciences morales 

 et politiques, sont susceptibles de 

 la meme certitude que celles qui 

 formeut le systeme des sciences 

 physiques, et meme que les 

 branches de ces sciences qui, comme 

 1 'astronomic, paroissent approcher 

 de la certitude mathematique. 

 Cette opinion lui e"tait chere, parce 

 qu'elle conduit a 1'esperance con- 

 solan te que 1'espece humaine fera 

 ndcessairement des progres vers le 

 bonheur et la perfection, comme 

 elle en a fait dans la connois- 

 sance de la verit^." It is evident 

 from this extract that Condorcet 

 (1743-94) thought that his friend 

 Turgot shared his own well-known 

 opinions as to the unlimited per- 

 fectibility of the human race. 



